Hopefully you named your topic "Oracle" otherwise we could think it is a MS/ACCESS question.
Oh wait... this is Oracle FAQ site... would be great if everyone give "Oracle" as title then we would be sure they don't post another kind of question.

What do you mean by You do not want to count manually by giving desc <table_name>. What do you want to count ? Do you want count the number of columns in a given table or do you want the count the number of rows in the given table. Either way you have to use the same function, but the source will vary depends on what you want to count ? For how to count the number of rows/columns read the oracle sql reference manual and search for the keyword count.